- #1

Bastian1978

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- TL;DR Summary
- I'm confused about how adding angular velocities works, in an example situation.

I'm trying to learn about adding angular velocities, and I'm confused about something. In this diagram...

https://i.sstatic.net/S6C03.png

there is a large orange disc rotating with angular velocity A (relative to the ground), and attached to the large orange disc is a small green disc, which is rotating at angular velocity B (relative to the large orange disc).

My understanding is that if I want to calculate the angular velocity of the small green disc, relative to the ground, then I would add A and B.

In the example I'm imagining, A is rotating anticlockwise at 1 radian per second, and B is rotating clockwise at 1 radian per second. So if I add A and B, I would get zero. I think that makes sense, since it'd mean that the orientation of the small green disc isn't changing relative to the ground.

The part that confuses me is that even though the orientation of the small green disc isn't changing relative to the ground (because its angular velocity relative to the ground is zero), if we imagine a point on the ground positioned at the centre of the large orange disc, the small green disc would be orbiting that point. So I don't understand how the green disc can be orbiting a point and yet have an angular velocity of zero?

I think I'm misunderstanding something fundamental about this, so if anyone could help me understand it better, that'd be great.

Also, I'd really appreciate being pointed to some reference material about this, particularly about how addition of angular velocity vectors works.

Thanks!

https://i.sstatic.net/S6C03.png

there is a large orange disc rotating with angular velocity A (relative to the ground), and attached to the large orange disc is a small green disc, which is rotating at angular velocity B (relative to the large orange disc).

My understanding is that if I want to calculate the angular velocity of the small green disc, relative to the ground, then I would add A and B.

In the example I'm imagining, A is rotating anticlockwise at 1 radian per second, and B is rotating clockwise at 1 radian per second. So if I add A and B, I would get zero. I think that makes sense, since it'd mean that the orientation of the small green disc isn't changing relative to the ground.

The part that confuses me is that even though the orientation of the small green disc isn't changing relative to the ground (because its angular velocity relative to the ground is zero), if we imagine a point on the ground positioned at the centre of the large orange disc, the small green disc would be orbiting that point. So I don't understand how the green disc can be orbiting a point and yet have an angular velocity of zero?

I think I'm misunderstanding something fundamental about this, so if anyone could help me understand it better, that'd be great.

Also, I'd really appreciate being pointed to some reference material about this, particularly about how addition of angular velocity vectors works.

Thanks!